The arithmetic mean, often simply referred to as the “mean,” is a fundamental concept in statistics and mathematics that represents the average value of a set of numbers. It is commonly calculated by adding up all the numbers in a dataset and then dividing the sum by the total number of values in the dataset.

In simpler terms, to find the arithmetic mean:

1. Add up all the numbers in the dataset.
2. Divide the sum by the total number of values.

Here’s a step-by-step example:

Suppose we have the dataset: 10, 15, 20, 25, 30.

1. Add up all the numbers: $10+15+20+25+30=100$.
2. Divide the sum by the total number of values (which is 5): 1005=205100​=20.

So, the arithmetic mean of the dataset is 20.

The arithmetic mean is widely used in various fields and contexts. It’s a measure of central tendency that provides an overall sense of the “typical” value in a dataset. However, it can be sensitive to extreme values (outliers) that can skew the average. In such cases, other measures of central tendency like the median or mode might be more appropriate.

Remember that the arithmetic mean is just one of many statistical measures used to describe and analyze data, and its appropriateness depends on the characteristics of the data and the goals of the analysis.